Problem: Rewrite as a simplified fraction. ${0.\overline{26} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 26.2626...\\ 1x &= 0.2626...\end{align*}}$ Subtracting the two equations, we have: ${99x = 26}$ ${x = \dfrac{26}{99}} $